Stable/unstable optical cavity resonator for laser

ABSTRACT

An improved resonator and optical cavity is adapted for use with a chemical laser that has a nozzle upstream of the resonator that emits a gain medium in a flow direction, and a pressure-recovery system downstream of the resonator. The optical resonator comprises first and second optical elements that are spaced apart from one another along an optical axis. Each of the optical elements has a selected geometry and a selected optical transmissivity to permit transmissive outcoupling of a beam of laser radiation from the resonator, the outcoupled beam being transmitted about the optical axis. The transmissivity and geometry of each optical element is selected to define an unstable region between the optical elements and around the optical axis, and a stable region in a region surrounding the unstable region and spaced apart from the optical axis.

CLAIM OF PRIORITY

This application is a continuation of U.S. patent application Ser. No.10/874,064, entitled “STABLE/UNSTABLE OPTICAL CAVITY RESONATOR FORLASER,” which was filed on Jun. 22, 2004 and which is herebyincorporated by reference for all purposes.

TECHNICAL FIELD

The present invention relates generally to optical cavities orresonators for laser apparatus. More particularly, the present inventionrelates to optical cavities or resonators for supersonic flow chemicallasers.

BACKGROUND

The invention of the gas dynamic CO₂ laser and, subsequently, the HF/DFlaser, indicated the feasibility of gas-flow lasers of high power. Theseare continuous wave (cw), supersonic flow devices, and, at a high-powerlevel, have a large saturated gain volume. An optical resonator orcavity is used to resonate photons from the gain volume into a coherentand collimated laser beam. Because the flow is supersonic, thecross-sectional area of this gain volume is roughly rectangular (ortrapezoidal) and not a disc. Because of this rectangular gain volume,conventional spherical optical elements in the resonator are difficultto use.

If the outcoupled beam from the resonator (the “laser beam”) isrectangular in cross section, it requires clipping and manipulation totransform it into one with a circular cross section. For a laser system,this process is costly and reduces the beam's power. On the other hand,if the beam emanating from the resonator or optical cavity has acircular cross section, then much of the radiative energy inside therectangular, box-like optical cavity may, unfortunately, contribute togas heating and/or parasitic lasing. It is, therefore, difficult tocouple the radiative energy in a box-like region into anaxially-symmetric outcoupled beam.

The first type of optical cavity or resonator that was used for a laseris referred to as a stable resonator and is described in Wrolstad, K.H., Avizonis, P. V. and Holmes, D. A., “Stable Resonators with IncreasedFundamental Mode Volume for CO2 Laser Oscillations” J. Phys., Part E, 4,pp. 143-145 (1971). This reference reports obtaining single transversemode operation (TEM₀₀) with CO₂ in a 1.2 cm diameter discharge tube.This beam size diameter, however, is far too small for use with a large,supersonic laser. With a stable resonator, it was realized thatoperation with a single, low-order mode was not possible. The laserwould be multi-mode, which results in an undesirable amount of beamspread when the beam is focused on a distant target. In addition,because the area of the gain volume is rectangular, a stable resonatormay fail to fully saturate all of the gain medium. Among other adverseeffects, destructive parasitic lasing can then ensue, especially for alarge, high-gain laser.

In a conventional chemical oxygen-iodine laser (COIL), the stagnationtemperature, static pressure, and Mach number M are about 300 K, a fewTorr, and about 2, respectively. The gas is largely helium with most ofthe balance being oxygen, some of which is in the excited ¹Δ electronicstate. The stagnation pressure for this gas is about 60 Torr.

Current COIL practice uses a gain medium that is linear rather thantoroidal. In the linear case, the mirrors are located at the far end oftwo optical ducts, away from the supersonic flow where the gain islocated. With a purge gas (helium), the ducts are maintained at aslightly higher pressure than the optical cavity to keep the mirrorsfrom degrading. Some means must be provided, such as a material oraerodynamic window, for transmitting the beam into the ambientatmosphere.

All current chemical lasers utilize an unstable resonator for a varietyof reasons that include the following important features:

(i) A large mode volume.

(ii) Transverse mode discrimination.

(iii) Single-ended output.

(iv) A confocal beam, if desired.

(v) A central main lobe in the far field.

(vi) The outcoupled beam stems from an annular portion of the coherentwave that is incident on the mirror. Nevertheless, the outcoupled beamis also coherent.

See Siegman, A. E., “Stabilizing Output with Unstable Resonator,” LaserFocus, 42, pp. 42-47 (May 1971) for an early discussion of the benefitsof this type of resonator. Krupke, W. F. and Sooy, W. R., “Properties ofan Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quant. Elect.,QE-5(12), pp. 575-586 (1969) describes a three mirror optical systemthat is current practice. All three mirrors are highly reflective andthe resulting beam is toroidal, i.e., in the near field the beam has ahole in it.

To outcouple a beam, current unstable resonators typically use thediffractive loss from the outer portion of a mirrored surface. In thefar field, the hole fills in, but as a result of its annular origin, theside lobes contain a larger fraction of the power than if the beamoriginated from a uniformly illuminated disc with a diameter equal tothe outer annular diameter. FIGS. 1 and 2 illustrate schematically thesetypes of resonators, with the lines having arrows representing theoutcoupled beam. In FIG. 1, the outcoupled beam simply diffracts aroundthe smaller mirror. In FIG. 2, a “scraper” mirror is used to outcouple abeam. In both cases, the outcoupled beam in the “near field” (close tothe resonator) is annular or donut-shaped. In the “far field” (adistance from the resonator), the beam “fills in,” but does not have anoptimal energy distribution.

As mentioned, the saturated gain region is generally box-like in a gasflow laser. There is a misfit between the geometry of this region and anaxially symmetric outcoupled beam. In a large laser, this misfit canresult in nonuniform saturation of the gain region. A poorly saturatedpart of the region, means, at least, some loss of laser power, or, atworst, destructive parasitic lasing. On the other hand, more nearlyuniform saturation poses the risk of optically coupling gain andabsorption regions. The loss of power may be severe when this happens.In this regard, each type of chemical laser is different. For instance,in COIL the absorbing state is the electronic ground state of the iodineatom. This atom is in its diatomic (non-absorbing) form when the fluidis in chemical equilibrium. Because of its low concentration, however,the three-body recombination rate of iodine atoms is slow. Hence, groundstate iodine atoms can remove energy from a coherent radiative field,and then lose this energy by spontaneous emission or collisionaldeactivation. This loss process can occur in the absorbing, supersonicflow just downstream of the saturated gain region.

Accordingly, a need exists for a resonator or optical cavity design thatis particularly adapted to the modern, supersonic flow chemical laser,in particular to the COIL.

SUMMARY

It is a general object of the present invention to provide an improvedresonator and optical cavity for use with a chemical laser andparticularly the COIL. This and other objects of the present inventionare achieved by providing an optical resonator for use with a chemicallaser that has a nozzle upstream of the resonator that emits a gainmedium in a flow direction. The optical resonator comprises first andsecond optical elements that are spaced along an optical axis. Theoptical axis intersects and includes the geometrical center of eachoptical element. Each of the optical elements has an opticaltransmissivity, an optical reflectivity, and a geometry selected topermit transmissive outcoupling of a beam of laser radiation from theresonator, the outcoupled beam being transmitted through an outcouplingregion in the first optical element that includes the optical axis.

According to the preferred embodiment of the present invention, thefirst optical element is at least partially transmissive and the secondoptical element is substantially completely reflective. The secondoptical element also has at least one surface region that is convex withrespect to the first optical element and at least one surface regionthat is concave with respect to the first optical element, wherein theoptical axis is transverse to the flow direction of the gain medium andthe second optical element is disposed exterior to the flow of the gainmedium.

According to the preferred embodiment of the present invention, thefirst optical element is a planar member formed of fused silica with apartial, gradient reflective coating that defines a circular outcouplingwindow or region coaxial and including the optical axis.

According to the preferred embodiment of the present invention, thesecond optical element is a high-reflectivity mirror.

According to the preferred embodiment of the present invention, thethird optical element is a planar member formed of fused silica.

According to the preferred embodiment of the present invention, theconvex surface region of the second optical element includes andintersects the optical axis and the concave regions are spaced apartfrom the optical axis.

According to the preferred embodiment of the present invention, thefirst optical element forms a portion of a wall connecting the nozzleand the pressure-recovery system and is cooled by the flow of the gainmedium.

According to the preferred embodiment of the present invention, a thirdoptical element is disposed along the optical axis between the first andsecond optical elements, the first and third optical elementscooperating to form two walls of an optical chamber connecting thenozzle to a pressure-recovery system and is cooled by the flow of thegain medium.

According to the preferred embodiment of the present invention, thefirst and third optical elements are rectangular in the planeperpendicular to the optical axis.

According to the preferred embodiment of the present invention, thetransmissivity and geometry of each optical element is selected todefine an unstable region between the optical elements and around andincluding the optical axis, and a stable region in a region surroundingthe unstable region and spaced apart from the optical axis.

According to the preferred embodiment of the present invention, thelaser gain medium is a supersonic flow of singlet delta oxygen withiodine injected in a chemical oxygen-iodine laser.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic depiction of a prior-art resonator;

FIG. 2 is a schematic depiction of another prior-art resonatorconfiguration;

FIG. 3 is a block diagram of a chemical oxygen-iodine laser (COIL) inaccordance with the preferred embodiment of the present invention;

FIG. 4 is a schematic representation of a portion of the optical cavityor resonator according to the preferred embodiment of the presentinvention;

FIG. 5 is a schematic representation of the optical cavity or resonatoraccording to the preferred embodiment of the present invention;

FIG. 6 is a cross sectional view of the optical cavity of FIG. 3, takenalong section line 6-6 of FIG. 5; and

FIG. 7 is an elevation view of one embodiment of the physicalarrangement of the optical elements of the optical cavity or resonatoraccording to the preferred embodiment of the present invention.

DETAILED DESCRIPTION

In its simplest form, a laser cavity (optical cavity or resonator)consists of a gain medium enclosed by two spherical mirrors, where thesides of the cavity are open. “Resonator” refers to the reflection ofphotons between optical elements, while “cavity” refers to the physicalspace between the optical elements. The mirrors have a radius ofcurvature R_(i), a radius a_(i), reflectivities r_(i), and a separationdistance L. The radius of curvature R_(i) is positive if concave towardthe gain medium, and L exceeds the L_(g) gain length. A planar mirrorhas an infinite radius of curvature. The mirror reflectivity r_(i) isbounded 0<r_(i)≦1. Thus, if mirror M₁ has r₁=0.8, then 20% of theintensity incident on M₁ is absorbed by the mirror or transmittedthrough it. In steady-state operation, this loss would be compensatedfor by amplification of the intensity by the gain medium. It is usefulto note that r_(i) can vary with location on mirror M_(i).

The geometrical stability of a resonator is determined by the gparameters

${g_{i} = {1 - \frac{L}{R_{i}}}},{i = 1},2.$If 0≦g₁g₂≦1 the resonator is stable; otherwise it is unstable. (Siegman)It is neutrally stable if g₁g₂ equals zero or unity.

FIG. 3 is a block diagram of a chemical oxygen-iodine laser (COIL) ofthe type contemplated by the present invention. The laser systemgenerally comprises a singlet delta oxygen (gas) generator 7 (SOG), anozzle 9, an optical cavity or resonator 11, and a pressure recoverysystem 13. Generated singlet delta oxygen has iodine injected and isaccelerated to supersonic velocity by nozzle 9. The supersonic gas flowis employed as the laser gain medium in an optical cavity or resonator11. The elements of the COIL illustrated in FIG. 3 are reasonablyrepresentative of the components of a supersonic flow chemical laser ofthe type the optical cavity or resonator according to the presentinvention contemplates.

Optical cavity or resonator 11 has an output of radiant energy(“outcoupled beam”) that is commonly referred to as the “laser beam”.The supersonic flow from optical cavity 11 has its velocity reduced andstatic pressure increased by a pressure recovery system 13, which maycomprise a diffuser or ejector or a combination of the two. A preferredSOG is described in commonly assigned application Ser. No. 10/453,148filed Jun. 3, 2003 entitled “Efficient Method and Device for GeneratingSinglet Delta Oxygen at an Elevated Pressure.” A preferred form ofnozzle and iodine injector is disclosed in commonly assigned applicationSer. No. 10/658,569, filed Sep. 9, 2003, entitled “Improved Laser Nozzleand Iodine Injection for COIL.” A preferred form of pressure recoverysystem of the diffuser type is disclosed in commonly assignedapplication Ser. No. 10/951,109, filed Jan. 4, 2005 and entitled“Supersonic Diffuser” and of the non-diffuser type in commonly assignedapplication Ser. No. 10/874,039, now U.S. Pat. No. 7,154,931, filed Jun22, 2004 and entitled “Laser With Brayton Cycle Pump.”

FIG. 4 depicts how resonator and cavity 11 fits in with upstream nozzle9 and downstream pressure-recovery system 13. The flow direction of thesupersonic gain medium is indicated by the arrow. A pair of opticalelements 21, 31 is planar, parallel, and merges smoothly with theupstream nozzle 9 wall surface and the downstream diffuser 13 wallsurface. As a consequence, resonator wall junctions do not generate anyaerodynamic disturbances. The upstream edge of optical elements 21, 31may extend into the laser nozzle region 9, wherein their surfaces becomepart of the nozzle's side walls. The location of the leading (trailing)edge of the optical system should coincide with, or be slightly upstream(downstream), of where saturated gain starts (ends). This is essentialin order to avoid parasitic lasing and to maximize the outcoupled power.In this regard, the optical system design automatically avoids thecoupling of positive and negative gain regions, as discussed below.

As will be described in greater detail with reference to FIGS. 5 through7, two of the three optical elements 21, 31, 41 making up resonator 11actually form the sidewalls of the optical cavity and are flush with thesides of the nozzle and diffuser. Each optical element is alignedthrough its geometric center, which is referred to as the optical axisof the resonator. Each optical element may be composed of a single lensor mirror, coated appropriately, or several lenses and mirrors bondedtogether, each of the lenses and mirrors performing the opticalfunctions described below.

FIG. 5 is a schematic diagram of the resonator configuration accordingto the preferred embodiment of the present invention, shown withoutsurrounding environment. The supersonic flow, with gain, is in thex-direction and is confined by planar and parallel surfaces 25, 33 of afirst optical elements 21 and a third optical element 31 and top andbottom surfaces of the optical cavity, which are similarly planar,parallel surfaces (not shown). There is a boundary layer, which may belaminar, on each of these surfaces. Saturated gain is confined to thebox-like region bounded by planar surfaces 25, 33 and those not shown.There is both flow and optical symmetry about the x-axis. The z-axisintersects the geometric center of each optical element 21, 31 and theelements are thus aligned along an optical axis (the z-axis). Generallyspeaking, the optical axis lies where the peak intensity of theradiation in the resonator (between first and second optical elements)is greatest. According to the preferred embodiment of the presentinvention, the optical axis coincides with the geometric centers ofrectangular optical elements 21, 31, 41. As will be further describedbelow, first and second optical elements 21, 41 are the opticallyfunctional elements of the resonator according to the present invention.As alluded to in FIG. 4 and described in greater detail below withreference to FIG. 7, third optical element 31 has only a “structural”function in the illustrated preferred embodiment and is purely opticallytransmissive. In other embodiments, this third element may have an“optical” function as well (i.e. have regions of variable reflectivityor surface 33).

As illustrated in FIG. 5, there are three optical elements, 21, 31 and41. Elements 21 and 31 are transmitting elements, while 41 has a highlyreflective coating on its surface 43. Adaptive optics can be used withoptical element 41, where the adjustments are made through the lowersurface 45. Because surface 43 is highly reflective, its substratematerial need not be specified or discussed. It is assumed that alloptical elements described have negligible, or nearly negligible,absorptivity.

As shown in FIG. 5, reflective optical element 41 has a pair (inactuality one that is circumferential about the z- or optical axis) ofconcave regions 47 (concave with respect to element 21 and the z- oroptical axis) and a convex 49 (again convex with respect to element 21and the z axis). The resonator is unstable in the vicinity of the z- oroptical axis where element 41 is convex 49, but becomes stable as x²+y²increases outward from the z axis, where element 41 is concave 47.Everywhere outside of d-diameter outcoupling window 27, the resonator isstable.

FIG. 6 is a plan view of optical element 21, taken along section line6-6 of FIG. 5. The surfaces of optical elements 21, 31 may extend verysmall distances a, b, beyond the gain region (the b distance may well bezero). An approximately axially symmetric outcoupled beam 51 (FIG. 7),of diameter d, where L_(x) and L_(y) are larger than d, exits theresonator through an outcoupling window 27 of diameter d formed inoptical element 21 as described below. This outcoupled beam 51 is theresult of “transmissive” outcoupling, as distinguished from thediffractive (FIG. 1) or reflective (FIG. 2) outcoupling of the priorart. A fully enclosed box-like region is contained between elements 31and 41.

For purposes of simplicity, the view in FIG. 6 shows a rectangularoptical element, rather than a tapered one (to correspond with aphysical taper between nozzle 9 and pressure-recovery system 13). Whichversion prevails depends on where the gain first becomes positive. Inthis embodiment, both first 21 and third 31 optical elements arerectangular in the plane perpendicular to the optical axis. In turn,this primarily depends on the location of the iodine injectors, whichare not shown in the Figures. If necessary, or desirable, taperedoptical elements can be avoided, e.g., by relocating the iodineinjectors downstream. The top and bottom walls connecting opticalelements 21 and 31 shown in FIG. 5 may each have a slight (0.5 degree toperhaps 4 degrees) outward angle to compensate for boundary-layer growthand any heat addition inside the laser cavity.

A variable reflectivity coating is on surface 25 such that it isessentially 100% reflective outside of the disc or window 27. Thus, thestable part of the resonator (outside window 27) has no outcoupling, butamplifies and feeds radiative energy inward into the unstable resonatorregion, which does have outcoupling through transmissive window 27.Although the tiny a and b regions may involve small-signal zero ornegative gain, there is little or no coupling between positive andnegative gain regions. This approach resolves the difficulties ofpositive/negative gain coupling, poor gain saturation or parasiticlasing, and the effective coupling of the radiant energy from a box-likevolume into an axially symmetric beam. Further, the delineation betweenoutcoupling window 27 and the remainder of surface 25 is illustrated asa sharp boundary, but it need not be. Outcoupling window 27 shouldinclude (intersect) the optical (z) axis and be symmetrical inconfiguration so that the outcoupled beam is similarly symmetrical aboutthe optical axis and includes the optical axis.

FIG. 7 illustrates a preferred arrangement for the optical cavityresonator according to the preferred embodiment of the presentinvention. As indicated schematically in FIG. 4, first and third opticalelements 21, 31 are formed and placed within, parallel to, and flushwith the sidewalls of the nozzle 9 and diffuser 13 (or otherpressure-recovery device). The supersonic gain medium then is availableto convectively cool the surfaces of these elements. Second opticalelement 41 is in a recessed cavity outside the flow of the gain medium.Because according to the preferred embodiment of the present invention,element 41 is ˜100% reflective, its energy absorption should not requirethe cooling necessary for transmissive elements 21, 31. The beam oflaser radiation (outcoupled beam 51) then is transmitted through window27 in element 21 transversely to the flow direction of the supersonicgain medium.

There is only a single set of modes for the stable/unstable resonator.The only loss mechanism is through the variable reflectivity coatingresulting in transmissive window 27, of diameter d, on element 21. Thissurface coincides with the unstable part of the resonator. Outcouplingis, therefore, transmissive, not diffractive. As with a conventionalunstable resonator, only a portion of the coherent incident wave isoutcoupled. As noted earlier for a conventional unstable resonator, theoutcoupled beam is still coherent. A large outcoupled fraction, as notedfor a conventional unstable resonator, selects the lowest-order modewhile suppressing higher-order modes. Thus, coherent outcoupled beam 51stems from a single, lowest-order mode for the stable/unstable resonatoraccording to the present invention.

Outcoupled beam 51 comes only from the unstable part of the resonator.In this region, the reflectivity of lower surface 25 of optical element21 smoothly varies. It changes from its minimum value on the optical orz axis, to effectively unity at the outer edge of window 27. The minimumvalue for the reflectivity is expected to be finite, but with a valuebelow 0.5. Because of the box-like gain region, the intensity variationof the wave incident on surface 25 may not be axially symmetric aboutthe optical axis. To compensate for this, the variable reflectivity inwindow 27 would not be radially symmetric. The distribution ofreflectivity can be adjusted so that the outcoupled beam 51 has anapproximate axially symmetric intensity profile.

In a conventional unstable resonator, the output aperture is nearlyuniformly illuminated and has side lobes in the far field. Resonator 11according to the preferred embodiment of the present invention has avariable reflectivity, and one or more of the surfaces of the opticalelements 21, 31, 41 may also have non-spherical curvatures. It ispossible to tailor the reflectivities and curvatures such that theoutcoupled beam has an axially symmetric, coherent, near gaussianintensity, or irradiance, profile without side lobes. This beam stemsfrom a single, lowest-order mode and contains the radiative energygenerated inside the box 29.

Between surfaces 23 and 43 the unstable oscillator contribution shouldcorrespond to a positive-branch mode in order to avoid the focusingeffect of the negative branch that could destroy the optical element 21,or 31, and cause breakdown in the gas in the focal point region. Thisshould be the case if g₁g₂≧1 on the z or optical axis. The outcoupledbeam 51 may be slightly converging or diverging. In other words, aconfocal beam may be advantageous but is not a requirement.

Shwartz, J., Nugent, J., Card, D., Wilson, G., Avidor, J. and Behar, E.,“Tactical High Energy Laser,” J. Directed Energy 1, pp. 35-47 (Fall2003) points out that a negative-branch unstable resonator has, relativeto a positive-branch unstable resonator, superior stability andalignment properties (stability here refers to the beam's stability, incontrast to the resonator's stability, previously discussed in terms ofthe g parameters). This negative-branch advantage, however, is largelylost for a stable/unstable positive branch resonator. Endo, M.,Kawakami, M., Takeda, S., Nanri, K. and Fujioka, T., “Theoretical andExperimental Investigation of Stable-Unstable Resonator Applied forChemical Oxygen-Iodine Laser,” Proc. SPIE, Gas and Chemical Lasers andIntense Beam Applications II, Vol. 3612, pp. 62-70 (1999).

The fully enclosed chamber between elements 31 and 41 can be filled withhelium at an average pressure based on the laser cavity and ambientpressures. This helps minimize the pressure loading on the opticalelements. Pressure loading on element 41 should not be a problem, sinceit is non-transmitting. Elements 21 and 31, however, are transmittingand must be able to handle their respective pressure loads. Theseelements are made from fused silica, discussed shortly, and theirthickness depends on their size and the structural load.

The thermal load on 21 and 31, caused by laser beam heating, iseffectively treated by the cooling properties of the mostly oxygen, ormostly oxygen plus helium, flow that is adjacent to surfaces 25 and 33.In this regard, it is advisable to keep iodine from condensing, oraccumulating, on surfaces 25, 33. This can be done by proper spacing ofthe two iodine injector struts closest to the side walls that containsurfaces 25 and 33.

FIGS. 4 through 7 assume the outcoupled beam exits through a window 27adjacent to the gas flow. It may be possible for the beam to exit at theother side of the resonator, through a transmissive window in element41. The illustrated configuration, however, is preferred, that justdescribed may not allow for adaptive optics.

It is preferable that the transmitting elements 21 and 31 survive in avery high radiative intensity environment. The following considerationsinsure that this is the case.

-   -   (i) Fused silica is used because of its very near unity value        for the bulk transmittance at 1.315 μm (the wavelength of COIL        radiation). Fused silica may not be unique in this regard. This        preferably is the IR grade fused silica with an extremely low H₂        O (see International Scientific Products Catalog, pp. 16 and 37,        2003).    -   (ii) The first and third optical elements 21, 31 in question are        very effectively cooled by the laser flow.    -   (iii) The resonator design according to the present invention is        free of a rapid intensity variation transverse to the beam's        axis. The two optical elements 21, 31 should, therefore, be free        of rapidly changing thermal gradients or of hot spots.    -   (iv) There is still an upper limit to the intensity that a fused        silica window can safely transmit (˜30 kW/cm²). To stay below        this limit, it may be necessary to increase the nozzle exit        height, L_(y), and the beam diameter, d, while simultaneously        keeping the overall power level fixed. This can be done by        keeping fixed the product of the O₂(¹Δ) partial pressure inside        the singlet oxygen generator (SOG) and the nozzle throat height.        The L_(y) and d lengths then increase by increasing the throat        height for a fixed nozzle area ratio. With the SOG pressure        decreasing, the diffuser recovered pressure decreases with this        approach. This is not necessarily the only design approach that        can be used to limit the maximum intensity on a transmitting        window.    -   (v) As the overall power of the laser beam increases, the        dimensions L_(y) and d (FIG. 6) can be increased such that the        maximum intensity on transmitting optical elements does not        increase. Thus, scaling from one power level to a higher one        does not necessarily imply a higher irradiance loading on the        transmitting elements. The preferred COIL can perform this        scaling in several ways. The simplest, and perhaps the most        effective, technique is to increase the throat height of the        laser nozzle now keeping the O₂(¹Δ) partial pressure, inside the        singlet oxygen generator, fixed. These changes increase        proportionately both the overall laser power and the nozzle exit        height, which is L_(y).    -   (vi) As previously noted, only a positive-branch resonator is        used.        The various constraints on first, second, and third optical        elements 21, 41, and 31 are now discussed in a general manner.        It is convenient to introduce the acronyms:    -   AR anti-reflection coating    -   CUR curved surface    -   PS planar surface    -   VRC variable reflectivity coating        In particular, a curved surface may, in fact, be planar,        spherical, or non-spherical. Based on the preceding discussion,        the surfaces of optical elements 21, 31, and 41 have the        following characteristics:

23 CUR, AR 25 PS, VRC 33 PS, VRC 35 CUR, VRC 43 CUR, ~100% reflectiveSurface 23 may actually be planar. Surfaces 25 and 33 are parallel. Avarying curvature is shown for surface 43. Thus, the reflectivity,transmissivity and geometry of each of the elements is selected so thattransmissive outcoupling occurs through a transmissive (capable oftransmitting rather than reflecting or absorbing radiation) window oroutcoupling region in one of the optical elements that includes theoptical axis and so that the geometrical portion of the resonatorsurrounding and including the optical axis is unstable and that portionof the resonator apart from the optical axis is stable. The illustrationof this surface is merely suggestive of a preferred embodiment thataccomplishes the goals.

The proposed approach has the important advantage of flexibility. Forinstance, an initial effort might have surfaces 23, 25, 33, and 35 asplanar and parallel. Surfaces 23, 33, and 35 would have AR coatings.Since element 31 is purely transmitting, its only function is to helpconfine the laser flow. Only surface 25 has a variable reflectivitycoating and only surface 43 has curvature. Moreover, as in Endo, surface43 could consist of inner and outer spherical surfaces of differentradii. The g parameters then satisfy g₂₅=1, and

$g_{43}^{\prime} = {{1 - \frac{L_{23} + L_{34}}{R_{43}^{\prime}}} > 1}$$g_{43}^{''} = {{1 - \frac{L_{23} + L_{34}}{R_{43}^{''}}} < 1}$where a prime (double prime) refers to an unstable (stable) oscillator.The g₄₃ value is for the positive branch, and yields a negative R′₄₃value for a mirror that is convex with respect to the gain medium, asexpected. The g″₄₃ value yields a positive R″₄₃ value for a mirror thatis concave with respect to the gain medium.

A reflective surface whose g parameters vary continuously with x and ycould be used. In this case, at the optical axis, g₁g₂≧1, and then g₁g₂decreases smoothly until, at the stable/unstable border, g₁g₂=1. Outsideof the border, g₁g₂ again decreases smoothly with x²+y², but remains inthe stable regime of 0≦g₁g₂<1. On the optical axis, the g parameters maycorrespond to a confocal oscillator.

Again, the preferred and illustrative embodiment has two “active” orfunctional optical elements 21, 41. Third optical element 31 is purelytransmissive and serves as a window and a structural component of theresonator according to the preferred embodiment of the presentinvention. As described immediately above, this is an exemplary case andvariations are possible.

Having thus described the present invention by reference to certain ofits preferred embodiments, it is noted that the embodiments disclosedare illustrative rather than limiting in nature and that a wide range ofvariations, modifications, changes, and substitutions are contemplatedin the foregoing disclosure and, in some instances, some features of thepresent invention may be employed without a corresponding use of theother features. Many such variations and modifications may be consideredobvious and desirable by those skilled in the art based upon a review ofthe foregoing description of preferred embodiments. Accordingly, it isappropriate that the appended claims be construed broadly and in amanner consistent with the scope of the invention.

1. An optical resonator for use with a chemical laser having a gainmedium with a direction of flow, the optical resonator comprising: aplurality of optical elements oriented along an optical axis with atleast one optical element being in fluid communication with and cooledby the gain medium, each optical element: having a plurality of opticalcharacteristics; and being selected for its optical characteristics andspaced relative to the other optical elements to permit transmissiveoutcoupling of a beam of laser radiation from the resonator through anoutcoupling region formed in one of the optical elements, theoutcoupling region surrounding the optical axis.
 2. The opticalresonator of claim 1, wherein the optical axis is perpendicular to thedirection of flow.
 3. The optical resonator of claim 1, wherein at leastone optical element is a high-reflectivity mirror.
 4. The opticalresonator of claim 1, wherein the plurality of optical elements furthercomprises: a first optical element that is at least partiallytransmissive; and a second optical element that is substantiallycompletely reflective and has at least one surface region that is convexwith respect to the first optical element and at least one surfaceregion that is concave with respect to the first optical element,wherein the optical axis is transverse to the flow direction of the gainmedium and the second optical element is disposed exterior to the flowof the gain medium.
 5. The optical resonator of claim 4, wherein theplurality of optical elements further comprises a third optical elementthat is a planar member formed of fused silica.
 6. The optical resonatorof claim 1, wherein the gain medium is a supersonic flow of singletdelta oxygen with iodine injected in a chemical oxygen-iodine laser. 7.An optical resonator comprising: a luminescent medium having a directionof flow; a plurality of optical elements that oriented along an opticalaxis with at least one optical element being in fluid communication withand cooled by the luminescent medium, each optical element: having aplurality of optical characteristics; and being selected for its opticalcharacteristics and spaced relative to the other optical elements topermit transmissive outcoupling of a beam of light from the resonatorthrough an outcoupling region formed in one of the optical elements, theoutcoupling region surrounding the optical axis.
 8. The opticalresonator of claim 7, wherein the optical axis is perpendicular to thedirection of flow.
 9. The optical resonator of claim 7, wherein at leastone optical element is a high-reflectivity mirror.
 10. The opticalresonator of claim 7, wherein the plurality of optical elements furthercomprises: the outcoupling region is defined in a first optical elementthat is at least partially transmissive; and a second optical elementthat is substantially completely reflective and has at least one surfaceregion that is convex with respect to the first optical element and atleast one surface region that is concave with respect to the firstoptical element, wherein the optical axis is transverse to the flowdirection of the gain medium and the second optical element is disposedexterior to the flow of the gain medium.
 11. The optical resonator ofclaim 10, wherein the plurality of optical elements further comprises athird optical element that is a planar member formed of fused silica.12. The optical resonator of claim 7, wherein the luminescent medium isa supersonic flow of singlet delta oxygen with iodine injected in achemical oxygen-iodine laser.